Title: Statistical Characteristics of High-Resolution COSMO Ensemble Forecasts in view of Data Assimilation
1Statistical Characteristics of High-Resolution
COSMO Ensemble Forecasts in view of Data
Assimilation
- Priority Project KENDA
- Daniel Leuenberger
- MeteoSwiss, Zurich, Switzerland
- COSMO GM 2009, Offenbach
2Introduction I
- General assumption in Ensemble Kalman Filter
MethodsErrors are of Gaussian nature and
bias-free - Prerequisite for
- optimal combination of model fc and
observations or - easily finding a minimum of the cost function
- How normal are these terms in the COSMO model?
3Non-Normality in EnKF
Pdf after update with stochastic EnKF
Pdf after update with deterministic EnKF
Lawson and Hansen, MWR (2004)
4Data
- Forecast departures (observation term)
- Different variables, observation systems,
heights, lead times and seasons - Based on a 3 month summer (2008) and winter
(2007/2008) period of operational COSMO-DE
forecasts - Ensemble anomalies (background term)
- Different variables, levels, lead times and days
- Based on 9 days (Aug. 2007) of the experimental
COSMO-DE EPS
5Evaluation Method
- PDF(qualitative)
- Normal Probability Plot(more quantitative)
6Example I Temperature
7Example II Rainfall
8General Findings for Observation Term
- Small deviations from normality around mean in
COSMO-DE for forecast departures of temperature,
wind and surface pressure out to 12h lead time
(normranges 80-95). - Fat tails, i.e. more large departures than
expected in a Gaussian distribution - Better fit in free atmosphere than near surface
- Deviation from normality in humidity and
precipitation - Transformed variables (log(pp) and NRH) have
better properties concerning normality and bias - Negligible differences COSMO-DE vs. COSMO-EU
- Slightly larger deviation from normality in a
sample of rainy days
9Ensemble Anomalies
- Background error calculated from ensemble spread
(anomalies around mean) - Look at distribution of ensemble anomalies of
COSMO-DE EPS forecasts - at 3h and 9h
- near surface and at 5400m above surface
- Example of 15.8.2007
- Time series of normranges over 9 days
10Ensemble Anomalies
Temperature at 10m, 3h (03UTC)
model physics perturbations
rlam_heat0.1
ECMWF
GME
NCEP
UM
11Ensemble Anomalies
Temperature at 10m, 9h (09UTC)
model physics perturbations
ECMWF
GME
NCEP
UM
12Ensemble Anomalies
13Timeseries of Normrange
Temperature
14Timeseries of Normrange
U component of wind
15General Findings for Background Term
- Larger deviations from normality than in
observation term (but smaller statistics, based
just on 9 summer days) - Smallest deviations in wind (normrange generally
70-90) - Larger deviations in
- temperature (20-90)
- specific humidity (60-80)
- precipitation (exponential distribution)
- Consistently better fit at 9h than at 3h
- Tendency for better fit in free atmosphere than
near surface
16Discussion
- Looked only at global distributions. Locally,
non-Gaussianity is expected to be more
significant (needs yet to be checked) - LETKF ensemble will differ from the current setup
of COSMO-DE EPS - Gaussian spread in initial conditions
- Non-gaussianity will grow during non-linear model
integration - For data assimilation more gaussian perturbations
will be needed - A final conclusion about non-Gaussianity of a
COSMO ensemble in view of the LETKF not possible
with current setup of COSMO-DE EPS
17Conclusions
- Observation term seems to be reasonably normally
distributed avaraged over many cases, except for
humidity and precipitation - Transformation of variables can improve normality
- High-resolution COSMO EPS might produce
non-normal anomalies in some cases - Will repeat such analyses with LETKF ensemble
- Ways to improve the LETKF in highly nonlinear /
non-normal conditions are currently being
investigated
18Thank you for your attention
19Example II Humidity from Radiosondes
20Ensemble Anomalies
Hourly Precipitation
3h 9h
21Ensemble Anomalies
Temperature at 5400m, 3h (03UTC)
model physics perturbations
ECMWF
GME
NCEP
UM
22Ensemble Anomalies
Hourly Precipitation, 3h (03UTC)
model physics perturbations
ECMWF
GME
NCEP
UM
23Ensemble Anomalies
Hourly Precipitation, 9h (09UTC)
model physics perturbations
ECMWF
GME
NCEP
UM
24Timeseries of Normrange
Specific humidity
25Methods to deal with Nonnormality
- No cost smoother (Kalnay et al., 2007)
- Apply weights from time t1 at time t
- Running in place
- Use observations more than once by iterating
several times over same assimilation window using
the no cost smoother until convergence - Outer loop in LETKF
- Bring analysis mean closer to observations by
iteration of update step (inner loop) - Advance to next assimilation time by using
nonlinear model (outer loop) using better guess
of mean analysis from inner loop - Have proven to improve LETKF in presence of
nonlinearity / non-Gaussianity in Lorenz model
(Yang and Kalnay, 2008)